I suggest reading David Fromkin's A Peace to End All Peace: The Fall of the Ottoman Empire and the Creation of the Modern Middle East.

Mr. Fromkin describes how and why the Allies, through the Sykes-Picot agreement, drew the lines of the Middle East. He also points to imperial ambitions and Europe's lack of understanding of the region's politics, religion, and culture.

http://www.goodreads.com/book/show/78107.A_Peace_to_End_All_Peace

This is, of course, a huge, and hugely important, question. I think there are two main things to keep in mind with regards to borders and the end of WWI:

1. The borders roughly agreed upon by Sykes-Picot, the Treaties of Sevres and Versailles, etc. (ie: the ones in which Europeans had the most say) were much more successful in setting general policies for governing Mandated territories (tutelary democracy or veiled colonialism, depending on your point of view) than they were setting very firm borders. Mostly because the Turkish War for Independence, ensuing instability between different Hashemite Monarchies in Syria and later Iraq, etc. etc., things weren't settled for awhile.

2. Once the borders were settled, which wasn't totally 100% finalized until 1938 when Alexandretta joined Turkey, they were more or less reflective of the international geopolitical order at the time. Imperial politics was still the order of the day -- while Turkey was no longer an imperial power, England and Russia still respected its leadership role in the region, leading to Turkey's prominence in such agreements as the Saadabad Pact (which was a pre-WWII version of what would become CENTO/Baghdad Pact), and the Straits were as important an issue as ever. Minority groups, like the Kurds, fell between the cracks of Turkish, French and English negotiations, and ultimately the Arab territories were devastated by WWI (famine hit Syria hard) and mounting any real military or political challenge to Britain/France in that time was difficult or impossible.

And I think these two things point more towards your second question: Why, if the borders were so haphazardly drawn (and no one is saying they weren't, vis-a-vis minorities), have they proved to be so stable? I think that answer, as I've suggested above, has a lot more to do with geopolitics, the run-up to WWII and the Cold War dynamic than anything else. In the Cold War, the US, through the Marshall Plan, made a real effort to support the independent regimes that came into power in Syria, Iraq and Turkey as (capitalist) buffers against the USSR. There's of course a lot of history going on in that relationship, and a lot happening behind the scenes and underneath the surface, but that's I think the best sketch I can give in a short amount of space.

As Margaret McMillan points out in her book, 'Paris: 1919', the British prime minister, Lloyd George, was concerned with how the Turks would be able to continue to govern a heterogenous population. They were civilized but not yet organized and would, therefore, need outside guidance. As a result, he thought that Britain should take the responsibility of preventing the different ethnicities from attacking each other. What prevented this from coming into fruition was the enormous costs associated with the occupation. Colonel House expressed to him that the United States would not be able to occupy the Turkish proper and Armenia if asked since this would go against WIlson's Fourteen Points. But based on these articles, it was assumed that the US would take control of the Bosphorus Straits and declare a mandate over Armenia. There were many mandates and agreements and proposed idea and if they were all implemented, " a very odd little Turkey in the interior of ANatolia would have been left, with no straits, no Mediterranean coast, a truncated Black sea coast, and no Armenia or Kurdish territories in the north east." The fate of the empire was further complicated by the secret treaty with Italy in 1915 which promised them with a sizeable portion of the Ottoman Empire. Greece was also promised eastern Anatolia becuase of the large presence of Greek settlers in the region but this conflicted with Italy's promise of a presence in the region by England and France. When occupation did take place in Turkey, this created a nationalist movement led by Atatürk that threatened stability in the region. This concern was supported by Churchill and Edwin Montagu (State Secretary of India) who warned that a partition of Turkey would appear to look like a war with the Muslim world. Additionally, any partition agreements quickly fell through because of power politics between Italy and Fr/GB. France had an interest in maintaining a unified Turkey because they held 60% of its debt. After the Wilson's failure to ratify the Versailles Treaty in Congress, the U.S. was officially withdrawn from any overseas agreements, especially in the Middle East. With the United States out of the way, the conference at San Remo had doen the following: the straits were under an international regime; France, Italy, and Greece had spheres of influence; Armenia was independent; a Kurdistan would be an autonomous region in Turkey. The enforcement of these spheres could not be accomplished since Ataturk was essentially "liberating" each region without much of a fight.